余倾斜余模和Hom-余倾斜余模的注记

本文证明了f-余倾斜余模的Bongartz引理,即一个偏f-余倾斜余模可以做成f-余倾斜余模.首先得到了f-余倾斜余模的性质以及C-余模和AT-模之间的函子同构.此外还研究了Hom-挠对和Hom-余倾斜余模.     

有限内射维数的余倾斜余模(英文)

本文中,受C.Nastasescu etc.和Y.Miyashita思想的影响,定义了余代数的余倾斜余模,研究得出有限内射维数的余倾斜余模的一些结论.     

关于伪紧余代数、余挠对和弦余代数

本文利用箭图和拓扑伪紧空间研究了K-余代数及其表示.定义了域K上的伪紧K-余代数,研究了伪紧K-余代数和K-代数范畴之间的关系,研究了余挠对和余模逼近,描述了余倾斜余挠对.通过有限维的支撑子余代数和基本的路余代数研究了弦余代数.     

余模分解与余代数分解的关系

设M是C-余模,C和M分别能被分解成不可分的子余代数和子余模的直和.给出这两个分解式之间的关系,从而给出了C的可约性和可分性与M的相关可约性和可分性之间的关系.     

Hom-可计算余代数的局部化

本文研究了可计算余模和Hom-可计算余代数的局部化问题.利用局部化方法,得到了可计算余模和Hom-可计算余代数的等价条件,推广了余代数上局部化理论的发展.     

余模范畴中的余倾斜预包络和余倾斜挠类

众所周知, Assem-Smal定理在倾斜理论中有重要的作用.本文的目的是建立一个在余模范畴中的Assem-Smal定理的版本,并通过利用预包络理论来刻画余模范畴中的余倾斜挠类.     

关于MH中的Lie双代数和余Poisson-Hopf代数

本文研究余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余ＰｏｉｓｓｏｎＨｏｐｆ代数,我们主要讨论余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数之间的关系。     

π-模余代数与π-模余理想

主要讨论局部有限维的Hopfπ-代数H上π-模余代数与π-模余理想.给出了π-H-模余代数与π-H~*-余模代数之间的对偶关系,得到了π-H-模余理想的一个充分必要条件.     

关于μ~H中的Lie双代数和余Poisson-Hopf代数(英文)

本文研究余三角 Ｈｏｐｆ代数余模范畴中的 Ｌｉｅ双代数和余 Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数．我们主要讨论余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数之间的关系．     

模余代数和Morita-Takeuchi关系

H是Hopf代数,C是H-模余代数.首先利用余积分的概念,诱导C的右H-余模结构,并构造了smash余积余代数C×H,使C×H作为余代数同构于C H.然后,由C的右H-余模结构诱导C的左H0-模结构,令C=C/KerεH0C,则C×H与C有Morita-Takeuchi关系.     

Gorenstein Cotilting and Tilting Modules

Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting modules in relative homological algebra considering subfunctors of the Ext-functor. In this article we generalize Auslander–Solberg relative notions by giving the definitions of infinitely generated Gorenstein cotilting and tilting modules by means of Gorenstein exact sequences. Using the theory developed by Enochs on the existence of Gorenstein preenvelopes and precovers, we prove a characterization of relative Gorenstein cotilting and tilting modules, which is a generalization of the beautiful characterization of relative cotilting and tilting modules given by Bazzoni.     

Cotilting modules are pure-injective

We prove that a cotilting module over an arbitrary ring is pure-injective.

     

Partial cotilting modules and the lattices induced by them

We study a duality between (infinitely generated) cotilting and tilting modules over an arbitrary ring. Dualizing a result of Bongartz, we show that a module P is partial cotilting iff P is a direct summand of a cotilting module C such that the left Ext-orthogonal class ⊥P coincides with ⊥C. As an application, we characterize all cotilting torsion-free classes. Each partial cotilting module P defines a lattice L = [Cogen P₁P] of torsion-free classes. Similarly, each partial tilting module P′ defines a lattice L′ = [[Gen P′,P′⊥]] of torsion classes. Generalizing a result of Assem and Kerner, we show that the elements of L are determined by their Rej_p-torsion parts, and the elements of L′ by their Tr_p-torsion-free parts.     

Hopf algebra deformations of binary polyhedral groups

We show that semisimple Hopf algebras having a self-dual faithful irreducible comodule of dimension 2 are always obtained as abelian extensions with quotient Z2. We prove that nontrivial Hopf algebras arising in this way can be regarded as deformations of binary polyhedral groups and describe its category of representations. We also prove a strengthening of a result of Nichols and Richmond on cosemisimple Hopf algebras with a two-dimensional irreducible comodule in the finite-dimensional context. Finally, we give some applications to the classification of certain classes of semisimple Hopf algebras.     

Tilting subcategories in extriangulated categories

Extriangulated category was introduced by H.Nakaoka and Y.Palu to give a unification of properties in exact categories anjd triangulated categories.A notion of tilting(resp.,cotilting)subcategories in an extriangulated category is defined in this paper.We give a Bazzoni characterization of tilting(resp.,cotilting)subcategories and obtain an Auslander-Reiten correspondence between tilting(resp.,cotilting)subcategories and coresolving covariantly(resp.,resolving contravariantly)finite subcatgories which are closed under direct summands and satisfy some cogenerating(resp.,generating)conditions.Applications of the results are given:we show that tilting(resp.,cotilting)subcategories defined here unify many previous works about tilting modules(subcategories)in module categories of Artin algebras and in abelian categories admitting a cotorsion triples;we also show that the results work for the triangulated categories with a proper class of triangles introduced by A.Beligiannis.     

New coefficients for Hopf Cyclic Cohomology

In this note, the categories of coefficients for Hopf cyclic cohomology of comodule algebras and comodule coalgebras are extended. We show that these new categories have two proper different subcategories where the smallest one is the known category of stable anti Yetter–Drinfeld modules. We prove that components of Hopf cyclic cohomology such as cup products work well with these new coefficients.     

Cleft Comodule Categories

We define crossed product categories and we show that they are equivalent with cleft comodule categories. We also prove that a comodule category is cleft if and only if it is Hopf–Galois and has a normal basis. As an application we show that the category of Hopf modules over a cleft linear category and the category of modules over the coinvariant subcategory are equivalent.     

On cohen-macaulay simplicial complexes

Let C be a coalgebra and let M be a right C-comodule. In this article we investigate the dimension of the space f of comodule morphisms from C to M. Our main result (Theorem 4) states that dim(∫_M)≤dim(M), for every left co-Frobeuius coalgebra (with some additional properties) and for every finite dimensional right comodule M. In particular, taking M = ki we obtain